Problem: Simplify the following expression: $\dfrac{120r^5}{36r^4}$ You can assume $r \neq 0$.
Answer: $ \dfrac{120r^5}{36r^4} = \dfrac{120}{36} \cdot \dfrac{r^5}{r^4} $ To simplify $\frac{120}{36}$ , find the greatest common factor (GCD) of $120$ and $36$ $120 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5$ $36 = 2 \cdot 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(120, 36) = 2 \cdot 2 \cdot 3 = 12 $ $ \dfrac{120}{36} \cdot \dfrac{r^5}{r^4} = \dfrac{12 \cdot 10}{12 \cdot 3} \cdot \dfrac{r^5}{r^4} $ $\phantom{ \dfrac{120}{36} \cdot \dfrac{5}{4}} = \dfrac{10}{3} \cdot \dfrac{r^5}{r^4} $ $ \dfrac{r^5}{r^4} = \dfrac{r \cdot r \cdot r \cdot r \cdot r}{r \cdot r \cdot r \cdot r} = r $ $ \dfrac{10}{3} \cdot r = \dfrac{10r}{3} $